MultiplicationTable - Maple Help
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LieAlgebras[MultiplicationTable] - display the multiplication table of a Lie algebra or a general non-commutative algebra

Calling Sequences

     MultiplicationTable(LieAlgebraName, keyword)

Parameters

     LieAlgebraName  - (optional) name or string, the name assigned to a Lie algebra

     keyword         - keyword string, one of "LieBracket", "ExteriorDerivative", "LieDerivative", "AlgebraTable"

 

Description

Examples

Description

• 

MultiplicationTable(LieAlgebraName, keyword) displays the form of structure equations for the Lie algebra or algebra dictated by the keyword.

• 

If the keyword is "LieBracket", then the Lie brackets of the basis elements are displayed in a two-dimensional array.

• 

If the keyword is "AlgebraTable", then the non-commutative products of the basis elements are displayed in a two-dimensional array.

• 

If the keyword is "ExteriorDerivative", then the exterior derivatives of the dual basis elements are printed.

• 

If the keyword is "LieDerivative", then the Lie derivatives  of the dual 1-forms  with respect to the basis vectors are displayed in a two-dimensional array.

• 

If LieAlgebraName is omitted, then the appropriate multiplication table of the current algebra is displayed.

• 

The command MultiplicationTable is part of the DifferentialGeometry:-LieAlgebras package.  It can be used in the form MultiplicationTable(...) only after executing the commands with(DifferentialGeometry) and with(LieAlgebras), but can always be used by executing DifferentialGeometry:-LieAlgebras:-MultiplicationTable(...).

Examples

 

Example 1.

First we initialize a 5 dimensional Lie algebra.

 

Display the Lie bracket multiplication table.

Alg1 > 

(2.1)

 

Display the exterior derivatives of the dual 1-forms.

Alg1 > 

(2.2)

 

Display the Lie derivatives of the dual 1-forms.

Alg1 > 

 

Example 2.

We initialize a 4 dimensional Lie algebra. Instead of using the standard default labels for the basis vectors we use and for the dual 1-forms we use .

Alg1 > 

Alg1 > 

 

Display the Lie bracket multiplication table.

Alg1 > 

(2.3)

 

Display the exterior derivatives of the dual 1-forms.

Alg1 > 

(2.4)

 

Display the Lie derivatives of the dual 1-forms.

Alg1 > 

 

Example 3. 

We initialize the quaternions  and display the multiplication table.

   

Alg1 > 

(2.5)
Alg1 > 

(2.6)
Alg1 > 

See Also

DifferentialGeometry

LieAlgebras

ExteriorDerivative

LieBracket

LieDerivative

 


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